Carefully use fine tweezers to grab the loose mesh and pull it outside.

The mesh is likely still stuck to one side of the ridge (assuming you pushed carefully), so it should be easy to retrieve. If not, locate it in the sound chamber and carefully remove it.

Make sure to not touch or damage the speaker membrane further in the back. Only use a small, soft brush if the mesh is stuck on the back side of the sound chamber.

Most of the glue should have come out together with the mesh. If necessary, carefully remove any remaining residue with the tweezers or a soft brush.

Here's some of the sticky black glue.